# Bounds on the Approximation Power of Feedforward Neural Networks

arXiv: https://arxiv.org/abs/1806.11416 · HTML: https://mlsanity.com/paper/1806.11416/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 3 of 3)

- [On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem](https://mlsanity.com/paper/2308.05509/) (2023)
- [Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions](https://mlsanity.com/paper/2312.14276/) (2023)
- [Approximating Probability Distributions by ReLU Networks](https://mlsanity.com/paper/2101.09973/) (2021)

## Abstract (arXiv)

The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth and width. These bounds improve upon state-of-the-art bounds for certain classes of functions, such as strongly convex functions. Second, an upper bound is established on the difference of two neural networks with identical weights but different activation functions.